Definition:Inscribe

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Definition

Let a geometric figure $A$ be constructed in the interior of another geometric figure $B$ such that:

$(1): \quad$ $A$ and $B$ have points in common
$(2): \quad$ No part of $A$ is outside $B$.

Then $A$ is inscribed inside $B$.


Circle in Polygon

A circle is inscribed in a polygon when it is tangent to each of the sides of that polygon:

Inscribe.png


Polygon in Circle

A polygon is inscribed in a circle when each of its vertices lies on the circumference of the circle:

Circumscribe.png


Polygon in Polygon

A polygon is inscribed in another polygon when each of its vertices lies on the corresponding side of the other polygon.


Polyhedron in Sphere

A polyhedron is inscribed in a sphere when each of its vertices lies on the surface of the sphere.


Sphere in Polyhedron

A sphere is inscribed in a polyhedron when it is tangent to each of the faces of that polyhedron.


Also see


Sources